How correct is the "Accuracy" value given by GPS devices?

The "accuracy" figure displayed by your GPS receiver will most likely be fairly reliable, but it can also be 'way off'.

It isn't "accuracy" that the GPS is displaying - it is the EPE, which is the Estimated Position Error. In other words, it is the probability that the location the GPS is displaying is within the "accuracy" distance from the true location.

Keep in mind that a GPS receiver doesn't actually know its true location. It calculates a location, based on the data received from the satellites (GPS receivers don't receive 'NMEA strings' from the satellites, but many can output NMEA sentences). While most GPS manuafacturers aren't going to tell you how they calculate "accuracy", you can consider it a figure that says "most of the time, the displayed location coordinates are within within X distance of the GPS receiver" (where X is the "accuracy" figure).

I'm surprised nobody mentioned CEP - Circular error probable. Actually the accuracy in meters provided by your GPS means that it's accurate within X meters from actual position 50% of the time!

https://en.wikipedia.org/wiki/Circular_error_probable

http://blog.oplopanax.ca/2012/11/your-gps-is-lying/

You can figure out the accuracy for yourself by calculating the RMS (root mean square) error by taking 10-20 readings of x-y coordinates over a known point (such as a survey monument) and applying a formula. THAT will tell you the true accuracy of your device BUT it will only pertain to that specific point in time that the coordiantes were collected. If you did the same test another time you may get a different answer due to cloud cover, tree cover (leaves vs. no leaves, or a tree grew or was cut down), and satellite position / number of satellites visible.